Answer to Question #47342 in Abstract Algebra for ayush kumar

Question

(a) Show that <x > is not a maximal ideal in z[x].

(b)List all the subgroups of Z18, along with 3 their generators.

(c)Let H=< (1 2) > and k = < (1 2 3) > be subgroups of S3. Show that S3 = Hk. Is S3 an internal direct product of H and k ? Justify your answer.

(d)Check whether or not { (2, 5), (1, 3), (5, 2), (3, 1) is an equivalence relation on { 1, 2, 3, 5 }.